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Journal of the Mechanical Behavior of Materials

Editor-in-Chief: Aifantis, Elias C.

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2191-0243
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Volume 22, Issue 1-2

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More hyperelastic models for rubber-like materials: consistent tangent operators and comparative study

Mokarram Hossain
  • Chair of Applied Mechanics, Department of Mechanical Engineering, University of Erlangen-Nuremberg, 5, D-91058, Erlangen, Germany
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Paul Steinmann
  • Corresponding author
  • Chair of Applied Mechanics, Department of Mechanical Engineering, University of Erlangen-Nuremberg, 5, D-91058, Erlangen, Germany
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2013-01-09 | DOI: https://doi.org/10.1515/jmbm-2012-0007

Abstract

Rubber-like materials can deform largely and nonlinearly upon loading, and they return to the initial configuration when the load is removed. Such rubber elasticity is achieved due to very flexible long-chain molecules and a three-dimensional network structure that is formed via cross-linking or entanglements between molecules. Over the years, to model the mechanical behavior of such randomly oriented microstructures, several phenomenological and micromechanically motivated network models for nearly incompressible hyperelastic polymeric materials have been proposed in the literature. To implement these models for polymeric material (undoubtedly with widespread engineering applications) in the finite element framework for solving a boundary value problem, one would require two important ingredients, i.e., the stress tensor and the consistent fourth-order tangent operator, where the latter is the result of linearization of the former. In our previous work, 14 such material models are reviewed by deriving the accurate stress tensors and tangent operators from a group of phenomenological and micromechanical models at large deformations. The current contribution will supplement some further important models that were not included in the previous work. For comparison of all selected models in reproducing the well-known Treloar data, the analytical expressions for the three homogeneous defomation modes, i.e., uniaxial tension, equibiaxial tension, and pure shear, have been derived and the performances of the models are analyzed.

Keywords: finite elasticity; hyperelasticity; micromechanical model; phenomenological model; rubber-like material; tangent operator

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About the article

Corresponding author: Paul Steinmann, Chair of Applied Mechanics, Department of Mechanical Engineering, University of Erlangen-Nuremberg, 5, D-91058, Erlangen, Germany


Published Online: 2013-01-09

Published in Print: 2013-06-01


Citation Information: Journal of the Mechanical Behavior of Materials, Volume 22, Issue 1-2, Pages 27–50, ISSN (Online) 2191-0243, ISSN (Print) 0334-8938, DOI: https://doi.org/10.1515/jmbm-2012-0007.

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